House Speaker John Boehner has offered to include higher tax rates on the wealthiest Americans as part of a deficit-reduction deal to avoid the fiscal cliff, a source close to the talks confirmed to CNN on Saturday.

The latest twist in the negotiations, first reported by Politico, indicates a possible breakthrough in the protracted efforts to forge a deal to reduce the nation's chronic federal deficits and debt.

According to the source, who spoke on condition of not being identified further, Boehner proposed allowing tax rates on income over $1 million to return to higher rates of the 1990s while extending current reduced rates for all income up to that threshold.

However, Boehner's spokesman said no deal had been reached, though communication continues with the White House.

Peter Lanza, father of Connecticut school shooting gunman Adam Lanza, released a statement Saturday expressing condolences to the families of victims.

“Our hearts go out to the families and friends who lost loved ones and to all those who were injured," Peter Lanza said. "Our family is grieving along with all those who have been affected by this enormous tragedy.

"No words can truly express how heartbroken we are. We are in a state of disbelief and trying to find whatever answers we can. We too are asking why. We have cooperated fully with law enforcement and will continue to do so. Like so many of you, we are saddened, but struggling to make sense of what has transpired.”

Police say Adam Lanza, 20, opened fire at Sandy Hook Elementary School in Newtown, Connecticut, on Friday morning, killing 20 students and six adults. Lanza also died at the school, authorities said.

Police also say Lanza's mother, Nancy Lanza, was killed at her house in Newtown before the school rampage began.

[Updated at 7:54 p.m. ET] Peter Lanza, father of alleged gunman Adam Lanza, released a statement Saturday expressing condolences to the families of victims.

"Our family is grieving along with all those who have been affected by this enormous tragedy. No words can truly express how heartbroken we are. We are in a state of disbelief and trying to find whatever answers we can," said the statement.

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